x^2+21x-228=0

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Solution for x^2+21x-228=0 equation: 


Simplifying
x2 + 21x + -228 = 0

Reorder the terms:
-228 + 21x + x2 = 0

Solving
-228 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '228' to each side of the equation.
-228 + 21x + 228 + x2 = 0 + 228

Reorder the terms:
-228 + 228 + 21x + x2 = 0 + 228

Combine like terms: -228 + 228 = 0
0 + 21x + x2 = 0 + 228
21x + x2 = 0 + 228

Combine like terms: 0 + 228 = 228
21x + x2 = 228

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 228 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 228 + 110.25

Combine like terms: 228 + 110.25 = 338.25
110.25 + 21x + x2 = 338.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 338.25

Calculate the square root of the right side: 18.391574158

Break this problem into two subproblems by setting 
(x + 10.5) equal to 18.391574158 and -18.391574158.


Subproblem 1
x + 10.5 = 18.391574158

Simplifying
x + 10.5 = 18.391574158

Reorder the terms:
10.5 + x = 18.391574158

Solving
10.5 + x = 18.391574158

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 18.391574158 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 18.391574158 + -10.5
x = 18.391574158 + -10.5

Combine like terms: 18.391574158 + -10.5 = 7.891574158
x = 7.891574158

Simplifying
x = 7.891574158


Subproblem 2
x + 10.5 = -18.391574158

Simplifying
x + 10.5 = -18.391574158

Reorder the terms:
10.5 + x = -18.391574158

Solving
10.5 + x = -18.391574158

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -18.391574158 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -18.391574158 + -10.5
x = -18.391574158 + -10.5

Combine like terms: -18.391574158 + -10.5 = -28.891574158
x = -28.891574158

Simplifying
x = -28.891574158


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.891574158, -28.891574158}

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